Question

a regular octagon is shown below. suppose that the octagon is rotated counterclockwise about its center so that the vertex at w is moved to u. how degrees does the octagon rotate?

Explanation:

Step1: Calculate the central angle of a regular octagon

The formula for the central angle of a regular \(n -\)sided polygon is \(\frac{360^{\circ}}{n}\). For an octagon, \(n = 8\). So the central angle \(\theta=\frac{360^{\circ}}{8}\).

$$ \theta = 45^{\circ} $$

Step2: Determine the rotation angle

When the vertex at \(W\) is moved to \(U\), it moves one - vertex position. Since the central angle between adjacent vertices of a regular octagon is \(45^{\circ}\), the octagon rotates \(45^{\circ}\).

Answer:

\(45^{\circ}\)